Three successive discounts of 20% each are equivalent to one discount

Question

Three successive discounts of 20% each are equivalent to one discount of what value?

A. 40%
B. 44%
C. 48.8%
D. 51.2%
E. 60%

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Dereno · Answer

This problem can be solved in multiple ways,

Method 1 : Ratio method.

20% is expressed as 1/5.

Three successive discounts means:

5 ————- 4

125 ————- 64.

= (125-64)/125

= (61/125) *100

=  48.8%

Method 2:

Successive discount = a + b + (ab/100)

With successive discount of 20%, we get

-20 -20 + (20*20)/100 = -40+4 = -36

again repeat the step with -36 and -20

-36-20 +( 36*20)/100

-56+7.2

- 48.8

Method 3:

100 * (4/5)*(4/5)*(4/5) = 256/5 = 51.2

Therefore, the discount is 100 - 51.2 = 48.8%

Option C

Edskore · Answer

Nice work by Dereno! Here's one more way to think about this that I found really fast during my prep — the  multiplier method .
 The idea:  A 20% discount means you pay 80% of the price, so the multiplier is 0.8.
Three successive 20% discounts means: Final price = Original × 0.8 × 0.8 × 0.8 = Original × 0.512
So you're paying 51.2% of the original price, which means the single equivalent discount is: 100% − 51.2% =  48.8% 
 Answer: C 
The trap answer is  60%  (choice E) — students who add 20 + 20 + 20 and don't understand that successive discounts compound, not add. Each discount applies to the already-reduced price, not the original.
Another trap is  44%  (choice B), which comes from incorrectly applying the successive discount formula for only two discounts.
 Takeaway:  For any successive percentage change problem on the GMAT, convert to multipliers (e.g., 20% increase = 1.2, 20% decrease = 0.8), chain-multiply, then convert back. It's the fastest and least error-prone approach.

vasu1104 · Answer

say initial price= 100x
value after 1st discount = 80x
value after 2nd discount = 64x
value after 3rd discount = 51.2x

now if we want to compare it with only one discount then we need to get 51.2x as value.

100x (p/100) = 51.2x
p = 51.2
that means its discount of 48.8 
choice C

Ujjwalk31 · Answer

100 * (4/5) * (4/5) * (4/5) = 256/5 = 51.2

Therefore, the discount is 100 - 51.2 = 48.8%

ANS = C

ExpertsGlobal5 · Answer

Video explanation:    https://www.youtube.com/watch?v=tg6ZmkescTM

luisdicampo · Answer

Deconstructing the Question

Each discount of   20\%   leaves   80\% = 0.8   of the price.

Successive discounts multiply.

Step-by-step

After first discount:

0.8

After second:

0.8 \cdot 0.8 = 0.64

After third:

0.64 \cdot 0.8 = 0.512

So   51.2\%   of the original price remains.

Total discount is

100\% - 51.2\% = 48.8\%

Answer: C

Three successive discounts of 20% each are equivalent to one discount

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GMAT Problem Solving (PS) Questions

Three successive discounts of 20% each are equivalent to one discount

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